analysis and perception in post-tonal music: an example...

Analysis and perception in post-tonal music: an examplefrom Kurtág’s String QuartetOp. 1

A R T I C L E

Psychology of Music

Psychology of MusicCopyright ©

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A N N A R I TA A D D E S S IU N I V E R S I T Y O F B O L O G N A , I TA L Y

R O B E RT O C AT E R I N AU N I V E R S I T Y O F B O L O G N A , I TA L Y

A B S T R A C T In this study, two different types of analysis of a piece of post-tonalmusic (the fifth movement of the String Quartet Op.1 (1959) by G. Kurtág) arecompared: an analysis performed by seven professional music analysts using themusical score, and a perceptual analysis carried out by two groups of subjects(18 musicians and 25 non-musicians) while listening in real time. Three possiblemacroforms proposed by the analysts were compared with those perceived by thelisteners. The results show that the macroforms hypothesized by the analysts represented the basic framework for those perceived by the listeners; moreover,the musical competence possessed by the musicians who took part in the listening exercise does not, on the whole, appear to have affected the perceptionof the macroform of a post-tonal piece of music.

K E Y W O R D S : categorization, contemporary music, cues abstraction, grammar, macroform, segmentations

Introduction1

The problems arising from the analysis of post-tonal music are very differentfrom those found in tonal music, both in terms of music theory (Forte, 1973;Hasty, 1981; Lerdahl, 1989), and the cognitive listening processes involved(Imberty, 1987, 1993; Deliège, 1989, 2001a, 2001b; Butler, 1990; Deliègeand El Ahmadi, 1990; Dibben, 1999). This is mainly, but not exclusively, onaccount of the lack of widely shared rules in post-tonal music. In this articlewe set out to compare the results of an analytical approach to the score of apiece of post-tonal music, with those of a perceptual analysis of the samepiece carried out in real time. The study is part of a wider project recentlylaunched by the Gruppo di Analisi e Teoria Musicale (GATM), a nationalresearch group based in the Department of Music at Bologna University,

sempre :

whose aim is to investigate the ‘macroform’ in post-tonal music, that is, theproblem of the overall form of a piece (Baroni, 2003).

General outline of the study

Generally speaking, it can be said that during the analysis of a score (or withthe aid of a score) certain analytic criteria are applied that derive from thecognitive listening processes, even though these are not always explicit orused systematically (Cross, 1998). In some cases, however, the analyst makesexplicit use of criteria deriving from the perceptual and cognitive processes ofan average listener, albeit a model listener (see Lerdhal and Jackendoff,1983). The issue of the perceptual pertinence of an analysis remains an openquestion that is still under discussion in theoretical studies (Nattiez, 1997;Lerdhal, 1997; Cross, 1998) and numerous investigations have been per-formed to examine the perceptual suppositions of certain analytical models(Deliège, 1987; Bigand et al., 1994; Dibben, 1999).

The present study can be placed somewhere between questions of a trulyanalytical nature on the one hand and the cognitive issues involved in real-time listening on the other. We investigate, for instance, whether the percep-tual criteria used by analysts when analyzing the macroform of a piece ofatonal music can be predictive of a listening situation and whether it is pos-sible to verify these criteria in such a situation. In addition, we try to find outif the musical competence of the listener, or his/her familiarity with the post-tonal repertoire, can influence the perception of macroform while listening inreal time.

GRAMMAR AND GRAMMATICAL COMPETENCE

To understand the distinction between the approach used by the analyst,even when attempting to perform a ‘perceptual’ analysis of a piece, and thatof the listener who tries to retain the piece of music in his/her mind, we referto previously formulated grammar theories (Lerdhal and Jackendoff, 1983;Baroni and Callegari, 1984; Johnsons-Laird, 1991; Baroni et al., 2003): ‘Therules of music, when explicitly formulated, are fundamentally a reflection onhow music is made and listened to, an attempt to describe rationally theorganization of sounds which a composer, a musician, a listener will put intoeffect when intuitively performing a musical activity’ (Baroni et al., 2003: 4).The relationship between the ‘grammar’ used by the analyst and the ‘gram-matical competence’ of the listener is that the former is an explicit renditionof the rules implicit in the latter. It should, of course, be born in mind thatwhen applied to the score such a ‘grammar’ loses certain elements character-istic of listening perception, which depend on temporal structures and theprocesses of memorization.

In the case of listening to post-tonal music, we are not always dealing withgrammatical rules as such. The procedures applied while listening to this type

Addessi and Caterina: Analysis and perception in post-tonal music 95

of music are often not based on pre-established systems of organizing soundthat are socially accepted and codified by common rules; it is true that insome cases certain rules deriving from the tonal tradition continue to work,while in other cases we are dealing with aspects of the language not based onculturally transmitted rules, but on experimental ideas which have not yetbeen ‘grammaticized’, whose perception may, however, sometimes be explainedin cognitive terms.

Nevertheless, the distinction between the intuitive competence of the listener and the explicit conceptualization of the analyst still holds true evenunder these conditions. The analyst tends to think in conceptual categories,transforming a categorical perception or simply a perception that obeys general cognitive laws, into definite concepts, even to the extent of settingthem in areas where such concepts have not yet been definitively codified bymusic theory.

Another essential difference between the listener and the analyst who putshim/herself in the place of a listener is that time, for the latter, is always freelyreversible. In a musical score, time is transformed into a space where it is pos-sible to stop at any point. Moreover, as Cook pointed out (1990), the visualperception of the score may also affect the analysis of the analyst as he/shelistens. In the context of our study, the analyst should nevertheless be awareof the perceptual difficulties and problems related to memory encountered bya listener and his/her task is precisely that of rendering these problemsexplicit (see also Cross, 1998). The analyst must therefore consider questionssuch as: what perception and memorization difficulties might the listener facein the piece I am analysing? Which structures can be clearly perceived?Which of them can be memorized?

SEGMENTATION AND MACROFORM

As already mentioned, the aim of the GATM project is to investigate the concept of macroform in post-tonal music. The term ‘macroform’ and theconcept we wish to identify by this term need to be carefully defined, sincethey are not always used in the same way (as is also the case with other musical terms).

By the term ‘macroform’, we refer to the global form of a piece, that is, thedivision of the piece into its largest parts with reference to its overall struc-ture. In musicological literature, various terms are used in a similar sense butwith meanings that are sometimes quite different, for example, ‘large dimen-sions’ (La Rue, 1970), or ‘large scale form’ (Levinson, 1997).2 In the field ofpsychology, Imberty (1981, 1993) uses the term ‘macrostructure’, whichoriginates from the field of linguistics (Kintsch and Van Dijk, 1975), but ishere considered from a perceptual point of view: a ‘scheme for structuringtime, where sound events are arranged a priori according to rules drawn fromthe perceptual mechanisms involved in the detection of changes within thecontinuum of sound’3 (Imberty, 1981: 90). Our use of the word basically

96 Psychology of Music 33(1)

derives from Imberty’s concept of macrostructure, but we have felt the needto distinguish between the concept of division into parts, which only identi-fies the macroform, and that of the perception of change, which we havedefined with the term ‘segmentation’. The importance of the process of seg-mentation and the identification of the criteria applied during this activity isan issue that has in fact been recognized in analytical studies ever since thefamous study by Ruwet (1966).

The reasons for choosing a particular segmentation vary considerably, butgenerally speaking they include: repetition (Ruwet, 1966), change or discon-tinuity (Imberty, 1981), rhythmic grouping (in metrically organized music,Lerdahl and Jackendoff, 1983) and the principles of difference and similarity(Deliège and Mélen, 1997; Deliège 2001a, 2001b). Although the term ‘segmentation’ is invariably used as a synonym for the division into parts, theanalysis carried out during the research of the GATM group has clearlyshown that segmentation is not a sufficient criterion to identify the mainparts of a piece (i.e. its macroform) since the perception of a strong local discontinuity does not necessarily produce a division in terms of the piece asa whole. A very long pause, for example, may give rise to the perception of asegmentation, but this does not necessarily constitute a separate self-contained section. On the other hand, parts of a piece can sometimes befound which are apparently different from one another even though there isno well-defined segmentation point dividing them.

The analysis of macroform poses different problems to that of segmenta-tion, especially where memory is concerned. The question is: when we reachthe end of the composition have we already mentally elaborated a possibledivision of the piece into parts? And are we able to say the exact number ofparts and identify them? Do we identify the parts as a result of their qualitiesand homogeneity or on the basis of local discontinuities? With regards totonal music, Deliège (Deliège and Mélen, 1997; Deliège, 1998) proposed aparticular experimental procedure, a ‘mental line’ that tries to test the abilityto memorize the quality and the order of succession of the parts identified ina piece while listening.

For the purposes of this article, then, the term ‘segmentation’ will be usedonly to indicate the exact point where two sections are separated, a local phenomenon brought about by the presence of a contrast or discontinuitythat involves one or more parameters of the musical material (duration,dynamics, timbre, density, register, etc.). The term ‘macroform’, on the otherhand, is used to indicate the result of a process of memorization involving thedivision of a piece of music into its largest parts, where each part has struc-tural coherence and homogeneity. As already mentioned, the macroform isnot necessarily brought about by the hierarchy of the segmentations.

Finally, one last remark should be made about the difference between the criteria involved in the division into parts of a post-tonal and a tonalpiece. In the former it appears to be, above all, a question of identifying


certain qualities of sameness and difference which can easily be perceivedand memorized, allowing the listener to abstract ‘cues’ (or prominent fea-tures) which distinguish one part of the piece from another (Deliège, 2001a).The division into parts of a tonal piece largely depends, however, on formal(and cultural) rules (exposition, development, conclusion, coda, recapitula-tion, bridge, repetition, symmetry, etc.). Traces of these cultural rules may, infact, persist in post-tonal music.

The GATM decided to focus its attention on the macroform of the piece,since it is basically the failure to perceive this aspect that may lead to confusion or tedium when listening to a post-tonal piece.

The experimental study

So far, the research has concentrated mainly on string quartets.4 By workingon such a homogeneous repertory, the number of variables is limited and it istherefore easier to formulate plausible and general hypotheses about theproblems of listening to post-tonal music.

A comparison is made here between the macroformal analysis of the fifthmovement of the String Quartet Op. 1, by G. Kurtág (Figure 1) carried out by seven professional music analysts from different Italian universities (mem-bers of the GATM) and those perceived by two groups of subjects, one madeup of musicians and the other non-musicians, while listening to the piece inreal time. The three macroforms selected for experimental study (see below)were the only ones to be proposed unanimously by all seven analysts afterworking independently on the basis of a pre-established analytical method.

For the reasons mentioned above regarding the differences between theanalysts and listeners, we do not necessarily expect the three solutions proposed by the analysts to be predictive of the behaviour of the listeners. Theaim of the study is rather to compare the two analytical procedures, that ofthe analysts and that of the listeners, in order to observe any elements theymight share and the differences that separate them.

THE ANALYSTS’ MACROFORM

The macroform analysis was largely based on Irène Deliège’s theory of ‘cueabstraction’ (see above), and on the theory of ‘domains’ proposed byChristopher Hasty (1981). The model proposed by Deliège for the mental representation of tonal and post-tonal music listened to in real time attemptsa systematic approach to these questions. Her hypothesis (see Deliège andMélen, 1997; Deliège, 2001a, 2001b) sees music perception as a vast processof categorization, which begins with the rhythmic grouping and the arrang-ing of groups based on the abstraction of ‘cues’, that is, the perception ofsimilarity between motifs located at different places in a piece, and culminatesin the organization of the traces left by the cues, the ‘imprints’.

A ‘domain’, on the other hand, may be described as a microelement, a


feature of the musical structure that presents constant values and unites dis-continuous elements, thus enabling a single section to be identified. Forexample, in Hasty’s analysis of Stefan Wolpe’s (1969) string quartet (Hasty,1981), the ‘domain’ is created in the first bar by the fact that the six notes areall introduced at regular eighth-note intervals, even though they present features of rhythmic, melodic and timbric discontinuity. However, since itmay occur that they are located in a context characterized by other featuresor domains, some of them presenting analogous constant values, the analystmust in this case make a decision about which of them is the most important.

The GATM group partly adapted Hasty’s idea to its own objectives.5 In apiece of music there are often sections where a given set of parameters (e.g.melodic intervals, characteristics of timbre, texture, dynamics, durations,etc.) behaves in a constant way. This persistence leads the listener to attributean internal unity to that section of the piece, which distinguishes it from asuccessive section when some, or all, of the parameters change their behav-iour. In other words, the characteristics of that particular parametric‘domain’ act as ‘cues’ (Deliège, 2001a) for the perception of the division intoparts. We should like to stress that, in our opinion, there is no conflictbetween the theories of Deliège and Hasty, since both of them attempt toidentify the reasons why a fragment is heard as a unit containing musicalcontinuity. While the analysts have time to seek out such points in the scoreand define them (referring to Hasty’s theory), the listeners have no such timeat their disposal and therefore depend more on the abstraction of ‘cues’ asproposed by Deliège.

In the piece by Kurtág, the above-mentioned analytical techniques had totake into account another important aspect: the presence of fragments characterized by an ostinato. This very evident feature may well be an exam-ple of the survival of certain aspects inherited from the tonal tradition (see,for example, the passacaglias of the 17th-century deriving from baroqueusage). The division into parts of the quartet therefore appears to dependlargely on the repetition of the ostinatos, following a principle that is quitesimilar to the one underlying classical structures, even though here we aredealing with ostinatos instead of themes. In this particular piece, then, the‘domains’ (the constant features of the timbres, dynamic, texture, etc.) that make up the homogeneous content of the sections, coincide with therhythmic-melodic ostinatos.

On the basis of the principle of the repetition of ostinatos and of the‘domains’, the analysts of the GATM group independently worked out the following three possible macroforms (see Table 1 and Figure 1):

● Macroform 1 – the analysts identified a first part, featuring a rhythmic-melodic ostinato that begins in bar 4 on the violin, although originatingin the rhythmic-harmonic double-stopping of the viola in bar 1. This firstostinato is repeated four times until bar 11, where the analysts indicate



(a)

(b)


F I G U R E 1 György Kurtág, String Quartet Op. 1, fifth movement (© 1964 Edito Musica, Budapest,Z.4481, pp. 21–26). Reproduced by permission of the publisher.

(c)

TA B L E 1 Analytical macroform hypotheses

Macroform 1I part bars 1–11 (sec. 000–27”/30”)II part bars 12–19 (3) (sec. 30”–50”)III part bars 19 (4)– 42 (sec. 50”– end)

Macroform 2I part bars 1–11 (sec. 000–27”/30”)II part bars 12–19 (3) (sec. 30”–50”)III part

IIIa bars 19 (4) – 29 (3) (sec. 50”–1’19”)IIIb bars 29 (4) – 42 (sec. 1’19”–end)

Macroform 3I part bars 1–11 (sec. 000–27”/30”)II part bars 12–19 (3) (sec. 30”–50”)III part

IIIa bars 19 (4) – 25 (1) (sec. 50”–1’7”)IIIb bars 25 (3) – 29 (3) (sec. 1’8”–1’19”)

IV part bars 29 (4) – 42 (sec. 1’19”– end)

the end of the first part. The second part features the entry of a new set ofostinatos, introduced by the double-stopping in syncopation with the second violin, beginning at bar 14 and ending at bar 18 (the passagefrom bars 12 to 14 without the ostinato was considered a bridge passageon account of its brief duration). The third part begins at bar 19 with theentry of a new ostinato played by the cello and the two violins, whichappears almost constantly until the end.

● Macroform 2 – the second proposed macroform takes into account thefact that the features of the last part of the piece are not completelyhomogeneous; from bars 19 to 29, the ostinato motive characteristic ofthis part is only repeated four times (bars 19, 21, 23 and 24); the thirdtime it is pianissimo and after the fourth time, the ostinato is followed byfive bars (25 to 29) where it does not appear at all; on the other hand,from bars 30 to 42, it is repeated eight times, each time closer (bars 30 to37) until finally being reduced in duration while being interspersed withlong pauses (bars 37 to 42). The second macroform, therefore, proposesthe division of the third part into two sections. The division between thetwo sections has been placed at bar 29, due to the long, pianissimo notes,which give the idea of closure.

● Macroform 3 – the last part of the piece could also be divided into threesections, if the five previously mentioned bars (25 to 29) are consideredas self-standing due to their not featuring any ostinatos. The third macro-form, therefore, proposes the division of the movement into four distinctparts.

It is interesting to note how the proposals have taken into account the factthat the presence of the ostinatos is not totally consistent. There are, as wehave seen, parts of the piece with no ostinatos. Moreover, the ostinatos them-selves present irregularities, mainly in the last part of the piece. Finally, thefact that the three proposed macroforms are somewhat different from oneanother should not be cause for surprise or for any doubts about the correct-ness of the procedure. It is simply due to the structure of the piece itself,which contains certain ambiguities and may be interpreted in more than oneway.

LISTENING TESTS

SubjectsTwo groups of subjects aged 22 to 35 took part in the experiment: 25 non-musicians (university students whose only musical experience was what theyhad received at school between the age of 11 and 14 years) and 18 musicians(conservatory graduates – piano, violin, composition, and conservatoryteachers – piano, composition, electronic music). Although the vast majorityof the musicians (70.6%) had previous experience of post-tonal music, only asmall group of non-musicians (21.4%) was familiar with the genre.


Materials The material used was G. Kurtág’s String Quartet Op. 1, fifth movement(1959), duration two minutes and two seconds, performed by the ArdittiString Quartet (CD WDR Auvidis Montagne MO 789007).

Apparatus A special computer program called EPM (Experiments on the Perception ofMusic) was used, which was devised at the University of Padua. This programallows each subject to listen to a piece through headphones and indicate thesegmentations perceived while listening in real time by clicking the mouse.Every time the mouse is clicked a red square on the screen in front of the sub-ject turns yellow. The program records the subject’s selection in hundredthsof seconds, making it possible to compare the results with the score (Figure 1).

Procedure Each subject was allocated a computer and given a questionnaire which, inaddition to the written answers, involved three tasks to be carried out usingthe EPM program. The questionnaire also contained details of how to use theprogram. The experiment took place in a room containing 30 computers. Thesubjects were called in two sessions of mixed groups (musicians and non-musicians) of 20 and 23. An operator read out the instructions for the use of the computers and the program. Two assistants were available to resolveindividual problems, if needed. Each test began only when all subjects hadfinished the previous task.

The experiment lasted approximately 45 minutes and involved varioussteps and tasks. After an initial listening to become familiar with the pieceand with the program (task 1), the subjects were given two segmentationtests: they had to listen to the piece twice and indicate during each listeningthe segmentations they perceived, using the computer and the EPM program(tasks 2 and 3).6 This was followed by two tasks involving the perception andmemorization of the macroform (tasks 4 and 5): the subjects had to listen tothe piece three times and identify the main sections; after the first listeningthey were instructed to mark the perceived sections along a line on a sheet ofpaper (task 4); in the next two listenings they had to indicate the sections onthe computer using the EPM program; that is, they were asked to indicate onthe computer what they remembered of the macroform of the piece (task 5).For the purposes of statistics, only the answers given for the last listening (thesixth listening) were considered.

In the next two tasks the subjects had to write the answers to questionsthat tried to identify the criteria they had used in formulating their solutions(tasks 6 and 7).

The results discussed in this article are based on the answers given in tasks5, 6 and 7, as they are directly concerned with the analysis of the macro-form.7


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TA B L E 2 Macroforms given by subjects and macroforms given by music analysts

93– 102– 109– 114–Seconds 1–7 8–13 14–25 26 27–34 35 36–41 42–46 47–54 55–56 57–65* 66–72 73–82 83–92 100 101 108 113 end

6– 11– 14– 16(4)– 18(4)– 25(2)– 37(1)– 37(4)– 40– 41(4)Bars 1–3 4–5 10(3) 10(4) 13(3) 13(4) 16(3) 18(3) 20 21 22–25* 27 28–30 31–33 34–36 37(3) 39 41(3) –42

Musicians1 X X X X X2 X X X X X X3 X X X X X4 X X X X X X X X X X X X5 X X X X6 X X X7 X X8 X X X9 X X X X X X10 X X X X11 X X X X12 X X X X X13 X1415 X X16 X X X X X X X X X17 X X X X X X18 X X X

Non-musicians1 X X X X2 X X X X X X3 X X X4 X X5 X X X6 X X X X X

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7 X X X8 X X9 X X X10 X X X X11 X X X X X X X12 X X X X13 X X X14 X X X15 X X X X X15 X X X17 X X X X X X X X18 X X X19 X X X X X20 X X X X21 X X X X X X X X22 X X X X X X X X23 X X X X X X X X X X24 X X X X25 X X X

Analysts’ macroformsMacroform 1 bar 12 bar 19(4)Macroform 2 bar 12 bar 19(4) bar 29 (3)Macroform 3 bar 12 bar 19(4) bar 25(2) bar 29 (3)

Difference musicians/non-musicians p < .05.The subjects’ replies are marked with the letter ‘X’. Bold X indicates the replies of the subjects that gave the identical macroform (musicians nn. 1and 3; non-musicians nn. 3 and 14).The answers given in test 5 have been grouped into 19 ranges corresponding to the areas where the subjects identified the points of division. Theranges are shown in the columns, with the seconds and bar numbers. In the last three lines, the bar numbers are given corresponding to thepoints where the analysts indicated divisions in their three macroform proposals. It is thus possible to see the macroform given by each subject(horizontally) and the extent to which they coincide with the solutions proposed by the analysts (vertically).

Results

TASK 5Generally speaking, the results show that the subjects’ perceptions of macro-forms were extremely heterogeneous. Most of the subjects, whether musi-cians or non-musicians, indicated more divisions than those hypothesized bythe analysts. The number of divisions indicated by each subject is extremelyvariable, ranging from 0 to 16. This makes any comparison between subjectsand between groups (musicians, non-musicians) somewhat problematic.

The answers given in task 5 have been grouped into 19 ranges (see Table2) corresponding to the areas where the subjects identified the points of divi-sion of the piece. It should be born in mind that Table 2 does not show precisepoints, but rather the number of seconds and the range of positions in the bar.The ranges therefore show the space of time where a set of answers is grouped.

In the data analysis, the dependent variables were the different ranges inwhich the answers are clustered and the independent variable was the musi-cal education of the subjects. A non-parametric test (Mann-Whitney) wasused to check the difference between musicians and non-musicians withinthe given ranges: only in the range 57–65 seconds, bars 22–25, do we find adifference that is statistically significant (Mann-Whitney U = 163, p < .05;see Table 2).

In order to observe the relationship between the perceived macroformsand the three macroforms of the analysts, it is necessary to analyse the datasubject by subject (see Table 2).

● Musicians – none of the musicians perceived a macroform which coincides perfectly with any of the three macroforms proposed by theanalysts. Only two subjects (numbers 1 and 3, see bold ‘X’ in Table 2)gave identical answers; that is, they perceived the same macroform.

● Non-musicians – we can see that there are two subjects (numbers 3 and14, see bold ‘X’ in Table 2) who perceived the same macroform. In thiscase, the macroform actually coincides with the analysts’ M2.

It is nevertheless possible to observe a general tendency confirming the pointsof division indicated by the analysts (see Table 2). The subjects thus con-firmed the analytical hypotheses, but with some variations. The division mostfrequently perceived (27–34 seconds, bars 11–13; musicians: 84.2%, non-musicians: 88.0%) coincides with the first point of division in the analysts’macroforms. The second most frequently perceived division (73–82 seconds,bars 28–30; musicians: 72.2%, non-musicians: 80.8%) only appears in M2and M3. The other division in the analysts’ macroforms, namely the one inbar 19(4) within the 47–54 seconds range, was less frequently indicated by the subjects (musicians: 44.4%; non-musicians: 46.2%). Finally, the pointof division in bar 25(2) within the 66–72 seconds range, which had beenindicated in M3, is completely absent in our subjects’ answers.


We developed an empirical index to check how near or far the macroformsperceived by the subjects were from those proposed by the analysts. All thepoints of division given for each perceived macroform were recorded andcompared with those of the analysts’ macroforms. In order to make this com-parison, the following formula was applied: I =(c*100)/A, where c is thenumber of points coinciding with the points in analysts’ macroforms and A isthe number of all the points of division indicated by the subjects. If A issmaller than the proposed points in the analysts’ macroforms then I is notcomputed.

It can be seen from Table 3 that M2 (I = 48.15 musicians; I = 52.41 non-musicians) is the closest to the macroforms perceived by both musicians andnon-musicians. The results for M3 are slightly lower (I = 47.85 musicians; I= 43.25 non-musicians), while M1 is clearly the furthest from the perceivedmacroforms (I = 28.96 musicians; I = 32.40 non-musicians). The resultsobtained for M1 can be explained by the fact that many subjects did not indicate the range 47–54 seconds as a point of division.

There are no significant differences in the I values between musicians andnon-musicians according to the Mann-Whitney test.

TASKS 6 AND 7In tasks 6 and 7, the subjects were asked to express the reasons for theirmacroformal choices. This was achieved by asking them to indicate, from alist of suggested items, the elements which had elicited their division of themusical piece into a certain number of parts; that is, they were asked to specifythe differences they had perceived between the various parts of their macro-forms. The following categories were considered:


TA B L E 3 Correspondence between macroforms proposed by musical analysts and macroforms perceived by the subjects

Mean index of StandardSubjects n correspondence* (%) deviation (%)

Musicians Macroform 1 16 28.96 15.79Macroform 2 14 48.15 18.33Macroform 3 12 47.85 18.59

Non-musicians Macroform 1 25 32.40 19.90Macroform 2 23 52.41 22.65Macroform 3 14 43.25 17.17

*Index of correspondence is an empirical measure that we have adopted obtained bythe number of points coincident with macroforms (1, 2 and 3) multiplied by 100 anddivided by the number of all the points given by the subjects to define their macro-forms. Reproduced by permission of the publisher.

1. variation in intensity; 2. timbre variation; 3. acceleration, deceleration or change in rhythm; 4. thickening or thinning of the sound; 5. introduction, repetition; 6. elements concluding or suspending;7. pause.

In task 6, subjects were asked to indicate all the elements they took intoconsideration. In task 7, subjects were asked to give a hierarchic order of theindicated elements (from the most important to the least important).

If we look at the results in Table 4, we can see that all the suggested cate-gories were used by our subjects to explain their segmentations. Some signifi-cant differences (p < .05), according to the Mann-Whitney test, can be foundbetween musicians and non-musicians: musicians in comparison with non-musicians seem to indicate the category ‘thickening or thinning of the sound’to explain segmentation in a larger number of cases; on the other hand thecategory ‘acceleration, deceleration or change in rhythm’ is significantlymore used by non-musicians.

If we consider the first categories chosen to explain segmentation (Table 5)we can see that it is the ‘timbre variation’ category which is the most frequently used by musicians, while ‘variation in intensity’ is the categorymost frequently adopted by non-musicians. According to the Mann-Whitneytest, a significant difference (p < .05) can be found between musicians andnon-musicians in the choice of the ‘timbre variation’ category, whereas thereis no significant difference between musicians and non-musicians in thechoice of the ‘variation in intensity’ category.

These results suggest that there may be some differences in the way musi-cians and non-musicians construct macroforms and that certain elementsare stressed more than others.


TA B L E 4 Closed answers: categories chosen to explain segmentation for the two groups ofsubjects (musicians = M, non-musicians = N).

Categories chosen to explain segmentation M (%) N (%)

1. Variation in intensity 66.7 78.62. Timbre variation 72.2 57.13. Acceleration, deceleration or change in rhythm 44.4* 75.0*4. Thickening or thinning of the sound 77.8* 50.0*5. Introduction, repetition 61.1 39.36. Elements concluding or suspending 66.7 57.77. Pause 50.0 71.4

*p < .05; **p < .01.

Discussion

Several interesting points concerning the perception of macroforms arisefrom Table 2, above all in relation to the results that are clearly very differentfrom the analysts’ solutions. For example, one of the points of division chosenby many subjects, involving the passage from bars 12 to 14, was not consid-ered suitable by the analysts, who, on account of its brevity, considered it as abridge passage lacking in independence. The subjects, on the other hand, per-ceived bars 12 to 14 (where the ostinato is suspended) as an independent sec-tion. The results show that the internal characteristics of the sections, andtherefore their homogeneity, seem to be more important for the listener thanthe duration of each section: the listeners seem to have been able to memo-rize not the presence of the ostinato, but rather its absence, and interpretedthis feature as a section. This finding coincides with the experience of Deliègeand El Ahmadi (1990): the listeners do not appear to have been influenced bythe duration of the parts, unlike the analysts, who are aware of the theoreti-cal principles of symmetry and formal balance. The question of experience ofelapsed duration in musical listening is, in fact, a very complicated and con-troversial issue which often depends on the structure of the events involved,as suggested by Jones (1990). The absence of the ostinato in bars 11–13would therefore seem to have acted as a ‘cue’, but it is nevertheless very likely,as the analysis of the closed answers suggest (tasks 6 and 7, Tables 4 and 5),that the listeners were also influenced by the concomitant changes in otherparameters, such as the intensity, the rhythm, the texture and the density ofthe sound. At bar 11(3), not only is there an interruption of the rhythmic-melodic ostinato, but there is also an evident change in various other param-eters (in particular an increase in the intensity and a change in texture),while at bar 14, the start of a new ostinato is accompanied by a markeddecrease in both the intensity and density of the sound, and a greater regu-larity in the organization of the durations.


TA B L E 5 Closed answers: first categories chosen to explain segmentation for the two groupsof subjects (musicians = M, non-musicians = N).

First categories chosen to explain segmentation M (%) N (%)

1. Variation in intensity 9.1 36.42. Timbre variation 36.4* 4.5*3. Acceleration, deceleration or change in rhythm 9.1 18.24. Thickening or thinning of the sound 9.1 13.75. Introduction, repetition 18.1 4.56. Elements concluding or suspending 9.1 4.57. Pause 9.1 18.2

*p < .05; **p < .01.

A similar occurrence can be observed in bar 25(2), where M3 proposes thebeginning of a new section (bars 25(2) to 29), characterized by the suspen-sion of the ostinato. Interestingly, in this case too about a third of the listenersperceive a brief section and indicate a point of division in bars 22–25. Thepoint of division indicated by the analysts is more precise, being based on thescore, and is situated on the second beat of bar 25. Nevertheless, the indica-tions given by the listeners in bars 22–23 lead us to hypothesize that the distinct change in intensity on the last beat of bar 22 may explain why the listeners decided to segment here, even though the ostinato, which began inbar 19, does not stop until bar 25. As in the previous case, then, it wouldappear that the listeners were not only influenced by the ostinato, but also byother parameters such as the intensity. And it is at this point that we find theonly significant difference between the musicians and the non-musicians (seeTable 2): it is the non-musicians in particular that indicate a division here,showing a greater accordance with the analysts.

Both M2 and M3 give the beginning of a new section at the end of bar 29,where an ostinato returns. Many of the listeners, however, marked the begin-ning of a new section at bars 31–33, perhaps wanting to be sure the newostinato was actually beginning, as they only registered the division after ithad been repeated twice. A similar situation was observed even more frequently in the previous listening tasks dealing with segmentation (not dis-cussed in this article), and this leads us to conclude that most of the subjectsare able to anticipate the beginning of the section at bar 29 only after severallistenings (6). This phenomenon has been studied by Deliège and El Ahmadi,who described this lapse of time between the end of the section and the segmentation as ‘tiling’ zones (‘the limits of the end of sections [. . .] and thesegmentations’, 1990: 25).

It is also interesting to note that the division marked by the analysts at thispoint coincides exactly with the start of the ostinato (bar 29(3)). Many of thelisteners, on the other hand, indicate the beginning of the new section at bar28, where we find a ‘sub. pp’, together with harmonics and long notes: amoment of calm contrasting with the convulsive density of the previous passage. Once again we see that for some of the listeners the macroform is notestablished by a thematic criterion (the rhythmic-melodic ostinato), butrather by the change in intensity, speed and density of sound (tasks 6 and 7,Tables 4 and 5).

Finally, another difference between the macroforms of the analysts andthose of the listeners can be found in the sections indicated in the final bars(37(4) until the end), where a large number of subjects indicated a divisionnot proposed by the analysts. The presence of the pauses certainly creates astrong case for contrast between one repetition and another in the same ostinato, a situation similar to the one described by Deliège in her studies onthe relationship between the principle of difference (pause) and the principleof similarity (repetition of the same ostinato) (Deliège and Mélen, 1997). One


may wonder, however, if the pauses alone are enough to create these sections, or whether their rhetorical function of bringing the piece to a closeis in some way involved.

Final remarks

In the present study, the results show that the distance between the analyticand listening procedures was not particularly great in the case of a scoreanalysis based on explicit criteria taken from theories dealing with perceptualaspects of sound: in our study we referred to the theory of cue abstraction(Deliège, 2001a and 2001b) and that of domains (Hasty, 1981). It hasalready been noted that, despite appearances, certain common patterns canclearly be identified. While not going so far as to say that the analysts’ solu-tions were predictive of the behaviour of the listeners, we can neverthelessobserve that the three macroforms proposed by the analysts do, to someextent, appear to have represented the basic framework for those perceived bythe listeners: the second macroform, in particular, represented a kind of aprototype that was perceived, with certain variations, by all listeners. Theabsence or repetition of the ostinatos acted as ‘cues’, as in the theoreticalmodel of Deliège.

One of the most interesting results is that it is clearly possible to renderexplicit the sense of continuity in a given part of a piece. It appears evidentthat the inner and predominantly unconscious intuition of elements of simi-larity, which give unity to a part, can actually be defined analytically bymeans of the presence of a set of domains. The listener, of course, does notalways have enough time to pick up such subtle structural aspects. On theother hand, certain structural devices, such as the ostinatos, are both welldefined analytically and easily perceived in listening. The notable presence ofostinatos in Kurtág’s quartet is, in fact, one of the reasons why the differencebetween the macroform analyses and listening responses was not so remark-able. Over and above the rhythmic-melodic parameter provided by the ostinato,however, other types of parameter also appear to have influenced the listeners: changes in the intensity and density of the sound, in the speed, andin the rhythm.

The differences between the analysts’ macroforms and those perceived bythe subjects of the experiment could in some ways be attributed to the differ-ent nature of the two types of analysis: the analysts referred to the musicalscore and so were able to make use of the visual aspect and go backwards andforwards to check their definition of the points of division and the homo-geneity of the various parts, enabling them in particular to pinpoint the exactpoints where an ostinato began and finished. The predominant criterion usedby the analysts was, then, the rhythmic-melodic aspect, and the use of thescore clearly facilitated this task. The subjects, on the other hand, performedtheir listening in real time and were thus subjected to the temporal cognitive


structures and were not influenced by the visual aspect. As a result their solu-tions were, as mentioned above, often determined by reference to otherparameters apart from the ostinato. A further important difference seems tobe that the analysts make much greater use of formal criteria transmittedculturally through their musical knowledge (e.g. symmetry and formal balance, use of structural criteria such as the bridge passage).

Finally, it is interesting to note that the subjects who were actually musi-cians did not generally seem to draw on their musical experience and this represents an unresolved problem worthy of further investigation. The differ-ences between the two groups of subjects, musicians and non-musicians,were not, apart from one exceptional case, statistically significant. This finding would therefore seem to support the hypothesis that, at some levels ofanalysis, the competence possessed by musicians does not neccessarily affectthe perception of the macroform of a piece, at least in the case of post-tonalmusic. The fact that most of the musicians had some familiarity with post-tonal music makes this aspect of our results all the more noteworthy.

In conclusion, the results obtained would to some extent seem to sustainour initial assumption: when the analysis of a written score is based on‘grammars’ inferred from the ‘grammatical competence’ of listeners, it is possible to produce analytical models that are fundamentally in line with aperceptual analysis whose cognitive mechanisms are described by theories ofpsychology.

N O T E S

1. Some of the data pertaining to this paper were presented at the SixthInternational Conference on Music Perception and Cognition, Keele, UK, 5–10August 2000.

2. There are undoubtedly many theoretical and analytical differences between theseauthors, and between these authors and ourselves, to the extent that a wholearticle could be dedicated to this issue alone. For this reason, we have decided torefer the reader to the literature and to mention here only the points that will helpclarify the contents of this article.

3. ‘Schéma de structuration du temps, c’est-à-dire mise en ordre a priori d’événementssonores, selon des règles issues des mécanismes perceptifs qui permettent lerepérage des changements dans le continu sonore’ (Imberty, 1981: 90).

4. A. Webern, String Quartet Op. 5; D. Milhaud, String Quartet No. 7; B. Maderna,String Quartet 1942 (alledged date) and Quartetto per archi in due tempi, 1955(Addessi and Caterina, 2000, 2002).

5. The theory of domains has also been the subject of a process of formalization bycomputer, but this will not be considered in this article (see D’Ambrosio et al.,1999).

6. This procedure was suggested by the experiment reported by Deliège and El Ahmadi (1990), and Deliège (1998). In our case there were three aims: tocompare the segmentations of the listeners in real time with those of the analystsusing the score; to observe any changes between the first and second segmen-tation (as in Deliège and El Ahmadi, 1990); to compare the results of the


segmentations with those of the division into parts (we should remember that inthis article the two terms are used with different meanings). The results of thesetwo tests will not, however, be discussed in this article, but are briefly mentionedin note 7.

7. The answers given in tasks 2 and 3 were analysed by taking into account the single seconds of the musical piece where our participants decided to indicate asegmentation point. As the number of individual differences was very high (someparticipants indicated a large number of segmentation points, while otherparticipants indicated only a very small number), we could not apply any globalmeasure, but had to limit ourselves to observing the differences between theanswers participants gave to single categories (i.e. seconds).

In any case, if we consider the mean number of segmentation points indicatedin tasks 2 and 3, we find that in task 2 the musicians indicated 15.72 segmenta-tion points, while the non-musicians indicated 16.83 points; in task 3, the figuresare respectively 16.8 points (musicians) and 16.48 points (non-musicians). Noneof these differences are significant according to the Mann-Whitney test. However,using the same test, significant differences were found between musicians andnon-musicians in several segmentation points (12 points) of task 2 and only in twopoints of task 3. In detail, the majority of non-musicians’ answers in task 2 appearon seconds 31 (p < .05), 64 (p < .05), 85 (p < .05), 103 (p < .05) and 117 (p < .05).On the other hand, most of the musicians’ answers fall on seconds 3 (p < .05) and 5(p < .05), and on seconds 52 (p < .05), 54 ( < .01), 66 (p < .05) and 84 (p < .05).

In task 3, the differences between musicians and non-musicians almost disap-pear. Significant differences only remain in two segmentation points: on seconds37 (p < .05) and 76 (p < .05). Neither second 37, nor second 76 scored a signifi-cant difference in task 2.

In task 3, the strongest segmentation points indicated by the non-musicianscoincided with the long pauses before the end of the piece (bar 40, second 109).The strongest segmentation for the musicians, on the other hand, was on bar 14(second 37), a point characterized not only by several pauses, but also by achange in texture and leading voice. It would appear that musicians pay moreattention to structural elements of compositions, whereas non-musicians seem tobe interested in surface elements (such as pauses). This may explain the signifi-cant difference found between the two groups on bar 14 (second 37).

We also present in the Table 6 the results deriving from the comparisonbetween the segmentations given during task 2 and those given during task 3, bymusicians as well as by non-musicians.

If the coinciding segmentation points in tasks 2 and 3 are considered, it can beseen that the correspondences between the two tasks expressed by musicians andnon-musicians are somewhat different. Only for seconds 84 and 116 do bothgroups express a concordance percentage which is above 60 percent. Percentagesof concordance are meant to indicate how coincident the segmentation pointsare in tasks 2 and 3 and in the groups of musicians and non-musicians.

However, a certain correspondence between the answers given in task 2 andthose given in task 3 can be seen for both musicians and non-musicians: if weconsider the means of the percentages of correspondences between the segmen-tation points of tasks 2 and 3, the mean for the musicians is 22.60, while for thenon-musicians it is 21.22. The difference between the means is not significantaccording to the Mann-Whitney test.

We can also observe that the answers given during the third listening are more


hierarchized in comparison with the previous one: briefer sections are groupedinto ampler sections, where important points of segmentation are singled out.During the third listening, the segmentation becomes more precise, anticipatingthe points of segmentation where the arrival of the change is already known: forexample, in the musicians’ group the point of segmentation shifts from 52–54seconds during the second listening to 50 seconds during the third listening andthe segmentation on second 105, at the long pause before the end (bar 38),almost disappears in the third listening, as its rhetorical effect has already beenmemorized and it no longer has any value as a segmentation.

A C K N O W L E D G E M E N T S

We would like to thank Cristian Temporali from Padua University, the author of theEPM program, and Fabio Regazzi from Bologna University for his technical assistance.We also thank Mike Webb, Petri Toiviainen, Nicola Dibben and the anonymous refer-ees for their suggestions during the drafting of this article.

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TA B L E 6 Coinciding points of segmentation in task 2 and in task 3 within the groups ofmusicians (18 subjects) and non-musicians (25 subjects)

Seconds Musicians (%) Non-musicians (%)

11 66.6725 85.7126 60.0036 61.5446 100.0053 66.6757 66.6760 100.0084 61.54 75.0093 66.67109 72.73116 66.67 66.67

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A N N A R I TA A D D E S S I , PhD in Systematic Musicology, is assistant professor at theUniversity of Bologna, where she teaches Music Education. Her main research inter-ests include cognitive musicology, involving auditive music analysis, music educationand artificial intelligence, training music teachers, musical style and intertextuality.She is author of many papers and books about music intertextuality (Claude Debussy eManuel de Falla: Un caso di influenza stilistica, CLUEB, 2000), music education and contemporary music (Le metamorfosi del suono: Idee per la didattica, EDT, 2000) andaesthetic and mass-media (Il giudizio estetico nell’epoca dei mass media, LIM, 2003). Herresearch has been presented at national and international congresses and publishedin scientific journals.Address: Department of Music and Performing Arts, University of Bologna, ViaBarberia 4, 40123 Bologna, Italy. [email: [email protected]]

RO B E RT O C AT E R I N A , PhD in Psychology, is a clinical psychologist and associate pro-fessor at the University of Bologna (Department of Psychology), where he teachesPsychology of Perception and Psychology of Music. He is a member of ESCOM and isparticularly interested in the relationship between music and emotional regulativeprocesses. Some results of his research into musical perceptual analysis, conducted incooperation with the Department of Music of the University of Bologna, have beenpresented at national and international congresses and published in international sci-entific journals.Address: Department of Psychology, University of Bologna, Viale Berti Pichat 5,40127 Bologna, Italy. [email: [email protected]]


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